where \(E_{ij} \in \mathbb {R}^{2 \times n}\)  with \(i\) th entry in row 1 and \(j\) th entry in row 2 being 1 and other entries being zero. It is clear that (REF ) is a set of linear constraints and (REF ) can be reformulated to a set of second-order constraints. Thus approximating \(\mathbb {S}^n_+\)  by \(DD_n\)  (\(SDD_n\)  respectively) in () becomes a linear program (second-order cone program, respectively), for which very efficient algorithms exist [1]}. This computational feature is one main motivation in the recent studies [2]}, [3]}.
